This textual content is meant for an honors calculus direction or for an advent to  research. related to rigorous research, computational dexterity, and a breadth of  purposes, it's perfect for undergraduate majors. This 3rd variation contains  corrections in addition to a few extra material.

Some gains of the textual content contain: The textual content is totally self-contained and begins with the true quantity  axioms; The vital is outlined because the zone less than the graph, whereas the world is  outlined for each subset of the airplane; there's a heavy emphasis on computational difficulties, from the high-school  quadratic formulation to the formulation for the by-product of the zeta functionality at  0; There are purposes from many components of study, e.g., convexity, the  Cantor set, endured fractions, the AGM, the theta and zeta functions,  transcendental numbers, the Bessel and gamma services, and lots of extra; ordinarily transcendentally awarded fabric, comparable to limitless  items, the Bernoulli sequence, and the zeta useful equation, is built  over the reals; and There are 385 issues of all of the strategies in the back of the text.

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